Nadia is 15 years younger than Ben. For the last 3 years, Ben and Nadia have been going to the same school. Sixteen years ago, Ben was 4 times as old as Nadia. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Ben and Nadia. Let Ben's current age be $b$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $b = n + 15$ Sixteen years ago, Ben was $b - 16$ years old, and Nadia was $n - 16$ years old. The information in the second sentence can be expressed in the following equation: $b - 16 = 4(n - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $n$ and substitute it into our second equation. Solving our first equation for $n$ , we get: $n = b - 15$ . Substituting this into our second equation, we get the equation: $b - 16 = 4($ $(b - 15)$ $ -$ $ 16)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 16 = 4b - 124$ Solving for $b$ , we get: $3 b = 108$ $b = 36$.